Related papers: Minimum Energy Problem on the Hypersphere
Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed…
The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and…
We use methods of approximation theory to find the absolute minima on the sphere of the potential of spherical $(2m-3)$-designs with a non-trivial index $2m$ that are contained in a union of $m$ parallel hyperplanes, $m\geq 2$, whose…
Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and…
We revisit the problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations where the matter model is a polytropic gas. We consider a…
Requiring that the baryon number of the universe be generated by anomalous electroweak interactions places strong constraints on the minimal supersymmetric standard model. In particular, the electric dipole moment of the neutron must be…
We calculate the low temperature corrections to the free energy for a sphere in front of a plane. First, the scalar field obeying Dirichet or Neumann boundary conditions is considered. Second, the electromagnetic field is studied, the…
By using the recently generalized version of Newton Shell Theorem analytical equations are derived to calculate the electric interaction energy between two separated charged spheres surrounded outside and inside by electrolyte. This…
Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential…
We consider the minimal action problem min \int\_R 1/2 |$\gamma$'|^2 + W($\gamma$) dt among curves lying in a non-locally-compact metric space and connecting two given zeros of W $\ge$ 0. For this problem, the optimal curves are usually…
The classical Stolarsky invariance principle connects the spherical cap $L^2$ discrepancy of a finite point set on the sphere to the pairwise sum of Euclidean distances between the points. In this paper we further explore and extend this…
A point charge in the presence of a metallic nanoshpere is a fundamental setup, which has implications for Raman scattering, enhancement of spontaneous emission of a molecule by an antenna, sensing, and modeling a metallic tip in proximity…
We present two methods for solving the electrostatics of point charges and multipoles on the surface of a sphere, \textit{i.e.} in the space $\mathcal{S}_{2}$, with applications to numerical simulations of two-dimensional polar fluids. In…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
Euclidean field theory on 4-dimensional sphere is suggested for the study of high energy multiparticle production. The singular classical field configurations are found in scalar and SU(2)-gauge theories and the cross section of 2->n…
A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from…
We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…
We study homogenization of a boundary obstacle problem on $ C^{1,\alpha} $ domain $D$ for some elliptic equations with uniformly elliptic coefficient matrices $\gamma$. For any $ \epsilon\in\mathbb{R}_+$, $\partial D=\Gamma \cup \Sigma$,…
In this paper, the overcharging problem and thermodynamics in the extended phase spaces of the five-dimensional spherically symmetric topological black holes are investigated by absorptions of scalar particles and fermions. The cosmological…
We consider an energy functional motivated by the celebrated $K_{13}$ problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional…